What will be the focus for this school year?
As a teacher, I am required to use the standards set by the state of California. For Reading Language Arts and Math, I have to follow the new Common Core State Standards (CCSS); for Science, the next Next Generations Science Standards (NGSS); for English Language Development (ELD), Social Studies, Arts, Health, and Physical Education, the California State Standards. Common Core State Standards also have literacy standards on other subjects including science, social studies and other technical subjects. The technology standards are also embedded on the Common Core State Standards. To learn more about these, click this page: www.mrreyes.org/curricular-areas/standards.
With the new Common Core State Standards, math has two sets of standards. The first is the content standard wherein CCSS clearly states what students need to learn on each grade. The second is what we call practice standards. These 8 mathematical practice standards are the same from kindergarten to 12th grade. So every time we have a lesson or an activity, I would refer to both content and practice standards.
This year, I have made Number Talks a priority. Although this daily classroom activity has many embedded math practice standards, I will just be focusing on math practice standards 3, 4, 5, and 6.
- MP3: Students should be able to explain their thinking and consider the thinking of others. This MP has different layers of expectations. I am focusing on the speaking and listening components. Students should be able to express themselves using words and also listen to what others are saying. I have not yet introduced the other layers of expectations. These are
- understanding what others are saying.
- analyzing what others are saying
- expressing their agreement or disagreement with another student
- applying what others have shared
- MP4 and MP5: Through Number Talks, I am hoping that students use different tools and ways to solve problems using pictures, symbols, objects, and words. I am now requiring students to show their solutions two ways PLUS the use of the number line, when appropriate.
- MP6: It did not really occur that because of Number talks, students are given opportunities to use learned vocabulary that will help them explain their thinking. Not knowing the correct terminology, students will just get frustrated explaining their thinking sometimes using or writing a whole paragraph that would have been avoided if the student knows the vocabulary. This also makes efficient use of their time.\
Lessons Learned so far:
The three properties of addition: associative, commutative, and identity properties of addition. This is how I explained these properties and the students have to learn these:
- associative property of addition:
- commutative property of addition:
- identity property of addition:
This week, I am focusing on addition strategies. The strategies we have so far are the following:
- additive identity: This has a fancy name. It just means that any number when added to zero (0), the number stays or the number retains its identity.
- For example:
- 5 + 0 = 5
- 0 + 5 = 5
- associative property of addition: Just remember, if 2 or more numbers are added together, the answer will always be the same no matter how these numbers are grouped.
- For example
- 2 + 3 + 4 = 9
- (2 + 3) + 4 = 9
- 2 + (3 + 4) = 9
- break apart: This strategy breaks double or triple digit numbers to their base place values.
- commutative property of addition: This is also known as flip the addends. If I know that 7 + 5 = 12. Then 5 + 7 should also be 12.
- compensation: I have not yet introduced this. This can lead to using other strategies like the doubles strategy.
- For example:
- 8 + 6
- If I subtract 1 from 8 (8 – 1 = 7)
- I then will add that 1 to the second number 6 (6 + 1 = 7)
- Can you see the doubles now?
- So 8 + 6 becomes 7 + 7 = 14
- Another example:
- 28 + 29
- I know I can make 29 to a 30 but I need to get that 1 from the 28.
- It should look like this (28 – 1) + (29 + 1)
- 27 + 30
- If I add 28 + 29, some studets will have a hard time adding the numbers in the ones place which is 8 and 9. It is easier to add 27 with 30 because the numbers in the ones place is 7 and 0.
- 27 + 30 = 57
- As a rule, if I take a number from one of the addends, I need to move them to the other addend so that the numbers do not really change. This is compensating.
- For example:
- counting on: Students may draw the number of items being added and then count all of these items to get the answer.
- doubles: Many students have already memorized their doubles facts. Just look at these songs and you’ll understand.
- doubles + 1: This capitalizes on students knowledge of the doubles facts.
- for example:
- 8 + 9 (9 can be expressed as 8 + 1)
- 8 + 8 + 1 (Can you see the doubles?)
- 16 + 1
- doubles – 1: This is the opposite of the doubles + 1. I have not introduced this yet but will only teach this to students who may find this easier than doubles + 1.
- for example:
- 8 + 9 (8 can be expressed as 9 – 1)
- 9 + 9 – 1 (Can you see the doubles?)
- 18 – 1
- flip the addends: If I know that 7 + 5 = 12. Then 5 + 7 should also be 12. This is also known as the commutative property of addition.
- landmark / friendly numbers: This is very similar to compensation but the focus is on using numbers that are easy to add. This is usually any sets of tens.
- For example:
- 18 + 5 may seem difficult
- I know that 20 is a landmark or friendly number. How do I know this? If I look at the number line, 20 is a number after 18 and I know the answer is more than 18 because I am adding.
- If I make 18 to 20, I have to add 2. Where do I get the two? I took the 2 from the 5.
- 18 + 5 becomes 20 + 3
- The total is 23.
- make a ten: This is a mental math strategy wherein students form tens and add the remainder to the ten to find the total.
- for example:
- 8 + 7
- choose the bigger number to create a ten
- 8 is the bigger number. To make a 10, I need 2 more.
- Where do I get the 2? 7 is the same as 2 + 5. If I take that 2 to add to 8, 8 becomes a 10, then that 7 becomes 5.
- 8 + 2 + 5
- 10 + 5
- make a ten using ten frame: This is for those who have difficulties with mental math. A ten frame is a template and also requires the use of beads or tokens or chips to manipulate. The student moves the beads from one ten frame to the other to create a 10. Then the student adds the 10 and the remaining beads from the other ten frame.
- number line: Number lines are big with CCSS. It seems like this is too easy but if students understand the concept of number lines, the lesson on integers will also be easy. Below is a very simplistic example of the use of number lines. starting this week, I am requiring my students to show their solutions using two strategies: the first is what they want to use (student’s choice). The second is the use of a number line (my choice!).
- part – part – whole model / bar model: The part – part – whole is also known as the bar model. Students who do not have the concept of addition or subtraction will draw the adddends. Each addend is in one box. These boxes are grouped to form the addend being represented.
Number Talks is a daily 15 minute activity where the teacher presents a problem and facilitates the discussion. The students are to share their strategies on how they got the answer. They have to use words to explain their thinking. My job is to clarify what the child is saying. I can then give that strategy a name and even model how to draw that strategy. This week, I am focusing on addition strategies. The strategies we have so far are the following:
CCSS Math Standards
California Mathematical Frameworks:
- Overview of the Standards Chapters
- Transitional Kindergarten
- The Curriculum Maps contain the standards as well as the Instructional Block(s) in which the standards will be taught and assessed. The Curriculum Maps can be thought of as a menu. It is not expected that one would do every lesson and activity from the instructional resources provided. And, like a menu, teachers select, based on instructional data, which lessons best fit the needs of their students – sometimes students need more time with a concept and at other times, less. Please read the Introduction_to_Elementary_Curriculum_Maps first.
- In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.
- In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.
- In grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.
- Introduction to the Grade 2 Curriculum Map The heading states 2014-2015 but the footer says revised June 2015.
- Second Grade Curriculum Maps, First 100 days, et. al: Again, the heading is 2014-2015 but the footer states revised June 2015.
- Grade 3 Instructional Guide contains the standards and Instructional Block(s) that would focus on four critical areas: (1) developing understanding of multiplication and division; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
- Grade 4 Instructional Guide contains the standards and Instructional Block(s) that would focus on three critical areas. Under the section Organized by Standards, the standards are listed as they are found in the Mathematics Framework for California Public Schools.
- Grade 5 Instructional Guide contains the standards and Instructional Block(s) that would focus on three critical areas. Under the section Organized by Standards, the standards are listed as they are found in the Mathematics Framework for California Public Schools.
- Online Module on the Grades 3-5 Curriculum Maps
- Fifth Grade Curriculum Maps, First 100 days, et. al
- What is number talks?
- How is it done?
- Is it CCSS aligned?
- What are the benefits of doing number talks?
- Where can I learn more about number talks?
- Blackline Masters: this site contains Microsoft Word and PDF files for download
- Illuminations: Designed by The National Council of Teachers of Mathematics(NCTM), Illuminations is the comprehensive source for instruction and learning materials based on NCTM’s Principles and Standards for School Mathematics. The site makes math engaging, interesting and challenging through interactive applets, standards-based lesson plans and other teacher resources.
- Illustrated Mathematics Dictionary
- InterActivate: is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions.
- LAUSD Math
- What Math Manipulatives to Use: What to use for what concept
- National Library of Virtual Manipulatives (NLVM): a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis)
- Sixty Second Sweep
- YouTube video explaining the 60 Second Sweep
- Sixty Second Sweep (pdf file: click to download)
- PowerPoint files